Alexander Lubotzky

Alexander Lubotzky
Name	Alexander Lubotzky
Birth date	1956
Birth place	Jerusalem
Nationality	Israel
Fields	Mathematics, Group theory, Lie groups
Institutions	Hebrew University of Jerusalem, Weizmann Institute of Science, Tel Aviv University, Institute for Advanced Study
Alma mater	Hebrew University of Jerusalem, Princeton University
Doctoral advisor	Grigory Margulis
Known for	Kazhdan's property (T), expander graphs, rigidity theory
Awards	Israel Prize, EMET Prize, European Mathematical Society prize

Alexander Lubotzky is an Israeli mathematician and public figure noted for contributions to group theory, Lie groups, and applications to combinatorics and computer science. He has held academic posts at major institutions and served in the Knesset and national advisory roles. His work links deep results in Kazhdan's property (T), superrigidity, arithmetic groups, and expander graphs with practical constructions used in theoretical computer science, coding theory, and cryptography.

Early life and education

Lubotzky was born in Jerusalem and completed early schooling before studying at the Hebrew University of Jerusalem, where he obtained undergraduate and graduate degrees. He pursued doctoral studies under Grigory Margulis at Princeton University, joining a lineage that includes influences from Yakov Sinai, Israel Gelfand, and the Soviet school of ergodic theory. His thesis connected to work of Margulis on arithmetic groups and the Oppenheim conjecture, situating him amid developments involving Harish-Chandra, John T. Tate, and Serre.

Academic career and positions

Lubotzky returned to Israel to take up positions at the Hebrew University of Jerusalem and the Weizmann Institute of Science, later affiliating with Tel Aviv University. He held visiting appointments at the Institute for Advanced Study, École Normale Supérieure, and universities such as Stanford University, University of Chicago, and University of Cambridge. He served on editorial boards of journals connected to Annals of Mathematics, Journal of the American Mathematical Society, and European publications, collaborating with researchers from Israel Institute of Technology, University of Oxford, and ETH Zurich.

Research contributions and mathematical work

Lubotzky's research spans group theory, representation theory, number theory, and combinatorial constructions. He made foundational contributions to the theory of property (T), influencing work by David Kazhdan, Shahar Mozes, and Yehuda Shalom. His studies of arithmetic groups and profinite groups built on techniques by Jean-Pierre Serre and Armand Borel, connecting to the Congruence Subgroup Problem explored by Hyman Bass and Gopal Prasad. Lubotzky co-developed constructions of explicit expander graphs using Ramanujan graphs theory and relations to automorphic forms, drawing on results by Amitai Regev, Peter Sarnak, and Alexander Selberg. These constructions impacted applications in theoretical computer science and network theory, echoing themes from Madhu Sudan, Noam Nisan, and Salil Vadhan.

In collaboration with colleagues such as Dan Segal, Martin W. Liebeck, and Yoshua Zalcstein, he advanced understanding of subgroup growth, subgroup rigidity, and profinite completions, relating to classical work of Emmy Noether, Helmut Hasse, and André Weil. Lubotzky's results on linear groups and subgroup separability influenced studies by Fritz Grunewald, Mikhail Gromov, and Jean Bourgain. His monographs and edited volumes synthesized developments linking superrigidity of Margulis, structural aspects of Lie groups studied by Elie Cartan, and modern combinatorial group theory.

Awards and honours

Lubotzky received the Israel Prize in mathematics and the EMET Prize for his scientific achievements. He has been awarded honors from the European Mathematical Society and elected to academies including the Israel Academy of Sciences and Humanities and international bodies such as the American Academy of Arts and Sciences. He lectured at distinguished venues such as the International Congress of Mathematicians and received fellowships from institutions including the Institute for Advanced Study and the Royal Society's associated programs. His citation list includes prizes alongside contemporaries like Grigori Perelman, Terence Tao, and Jean-Pierre Serre.

Political and public service

Beyond mathematics, Lubotzky served as a member of the Knesset representing Likud and participated in committees related to science and technology, interacting with ministries such as the Ministry of Science and Technology and institutions like the Council for Higher Education (Israel). He contributed to public debates alongside figures like Shimon Peres, Benjamin Netanyahu, and Ehud Barak on national policy for research and innovation. Lubotzky advised bodies including the Israel Science Foundation and international organizations linked to the European Research Council and engaged in outreach connecting mathematicians with policymakers and industry representatives such as those from Intel, Microsoft Research, and IBM Research.

Personal life and legacy

Lubotzky's family background ties to prominent Israeli cultural and academic networks, intersecting with personalities such as Hannah Arendt-era intellectuals and later generations of scholars. His students and collaborators include mathematicians who now hold positions at Princeton University, Harvard University, University of California, Berkeley, and Imperial College London. His legacy endures through textbooks, research monographs, and constructions used across computer science, cryptography, and pure mathematics, influencing ongoing work by researchers like Elon Lindenstrauss, Avi Wigderson, and László Babai.

Category:Israeli mathematicians Category:Group theorists